#### Volume 21, issue 4 (2017)

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Collar lemma for Hitchin representations

### Gye-Seon Lee and Tengren Zhang

Geometry & Topology 21 (2017) 2243–2280
##### Abstract

There is a classical result known as the collar lemma for hyperbolic surfaces. A consequence of the collar lemma is that if two closed curves $A$ and $B$ on a closed orientable hyperbolizable surface intersect each other, then there is an explicit lower bound for the length of $A$ in terms of the length of $B$, which holds for every hyperbolic structure on the surface. In this article, we prove an analog of the classical collar lemma in the setting of Hitchin representations.

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##### Keywords
hyperbolic surfaces, convex real projective surfaces, collar lemma, Hitchin representations
##### Mathematical Subject Classification 2010
Primary: 57M50
Secondary: 30F60, 32G15
##### Publication
Received: 22 December 2015
Revised: 10 July 2016
Accepted: 8 August 2016
Published: 19 May 2017
Proposed: Ian Agol
Seconded: Simon Donaldson, András I. Stipsicz
##### Authors
 Gye-Seon Lee Mathematisches Institut Ruprecht-Karls-Universität Heidelberg Im Neuenheimer Feld 205 D-69120 Heidelberg Germany http://www.mathi.uni-heidelberg.de/~lee/ Tengren Zhang Mathematics Department California Institute of Technology Mail Code 253-37 1200 East California Boulevard Pasadena, CA 91125 United States http://sites.google.com/site/tengren85/